Quantification of the thermodynamic effects of the low-spin - high-spin interaction in molecular crystals of a mononuclear iron(II) spin crossover complex

A method is proposed to estimate the energetic and entropic effects of spins of neighbouring molecules on the spin transition of a mononuclear spin crossover (SCO) complex in a molecular crystal. Density functional theory (DFT) methods have been used to model the SCO material [FeII(Lnpdtz)2(NCS)2] (Lnpdtz = 2-naphthyl-5-pyridyl-1,2,4-thiadiazole) exhibiting numerous π-π interactions using a 2D arrangement of 15 molecules. The modelling considers only the effects in the crystallographical ac plane with a particularly pronounced stacking but paves the way for future work with 3D arrangements which are computational much more costly. It involves the optimisation and normal mode calculation of the molecules in a rigid matrix of both low-spin (LS) and high-spin (HS) neighbours. This procedure has been used to calculate the previously defined cooperativity parameter Hcoop (S. Rackwitz, W. Klopper, V. Schünemann and J. A. Wolny, Phys. Chem. Chem. Phys., 2013, 15, 15450). For [FeII(Lnpdtz)2(NCS)] we obtain Hcoop = 11 kJ mol-1, a value which is comparable to those found for 3D polynuclear spin crossover materials. A normal mode analysis of the optimised centrally located molecule indicates that the vibrational entropy of the spin transition is somewhat higher (5 J K-1 mol-1) for the LS to HS transition in the LS matrix than in the HS one. The calculations show that the interactions with the neighbours influence the low-frequency modes with wave numbers <65-70 cm-1. These cause the main difference in the vibrational entropy of the spin transition for the vicinity of high- and low-spin molecules. Furthermore, a deformation of the coordination sphere of the central molecule is observed when the spins of the surrounding centres are switched. This deformation is accompanied by a change in the equatorial Fe-N bond lengths.

Tailoring light-induced charge transfer and intersystem crossing in FeCO using time-dependent spin-orbit configuration interaction

Real-time (RT) electronic structure methods provide a natural framework for describing light-matter interactions in arbitrary time-dependent electromagnetic fields (EMF). Optically induced excited state transitions are of particular interest, which require tuned EMF to drive population transfer to and from the specific state(s) of interest. Intersystem crossing, or spin-flip, may be driven through shaped EMF or laser pulses. These transitions can result in long-lived "spin-trapped" excited states, which are especially useful for materials requiring charge separation or protracted excited state lifetimes. Time-dependent configuration interaction (TDCI) is unique among RT methods in that it may be implemented in a basis of eigenstates, allowing for rapid propagation of the time-dependent Schrödinger equation. The recent spin-orbit TDCI (TD-SOCI) enables a real-time description of spin-flip dynamics in an arbitrary EMF and, therefore, provides an ideal framework for rational pulse design. The present study explores the mechanism of multiple spin-flip pathways for a model transition metal complex, FeCO, using shaped pulses designed to drive controlled intersystem crossing and charge transfer. These results show that extremely tunable excited state dynamics can be achieved by considering the dipole transition matrix elements between the states of interest.

Benchmarks for transition metal spin-state energetics: why and how to employ experimental reference data?

Accurate prediction of energy differences between alternative spin states of transition metal complexes is essential in computational (bio)inorganic chemistry-for example, in characterization of spin crossover materials and in the theoretical modeling of open-shell reaction mechanisms-but it remains one of the most compelling problems for quantum chemistry methods. A part of this challenge is to obtain reliable reference data for benchmark studies, as even the highest-level applicable methods are known to give divergent results. This Perspective discusses two possible approaches to method benchmarking for spin-state energetics: using either theoretically computed or experiment-derived reference data. With the focus on the latter approach, an extensive general review is provided for the available experimental data of spin-state energetics and their interpretations in the context of benchmark studies, targeting the possibility of back-correcting the vibrational effects and the influence of solvents or crystalline environments. With a growing amount of experience, these effects can be now not only qualitatively understood, but also quantitatively modeled, providing the way to derive nearly chemically accurate estimates of the electronic spin-state gaps to be used as benchmarks and advancing our understanding of the phenomena related to spin states in condensed phases.

Spin-State Splittings in 3d Transition-Metal Complexes Revisited: Benchmarking Approximate Methods for Adiabatic Spin-State Energy Differences in Fe(II) Complexes

The CASPT2+δMRCI composite approach reported in a companion paper has been extended and used to provide high-quality reference data for a series of adiabatic spin gaps (defined as ΔE = E_quintet - E_singlet) of [Fe^IIL₆]²⁺ complexes (L = CNH, CO, NCH, NH₃, H₂O), either at nonrelativistic level or including scalar relativistic effects. These highly accurate data have been used to evaluate the performance of various more approximate methods. Coupled-cluster theory with singles, doubles, and perturbative triples, CCSD(T), is found to agree well with the new reference data for Werner-type complexes but exhibits larger underestimates by up to 70 kJ/mol for the π-acceptor ligands, due to appreciable static correlation in the low-spin states of these systems. Widely used domain-based local CCSD(T) calculations, DLPNO-CCSD(T), are shown to depend very sensitively on the cutoff values used to construct the localized domains, and standard values are not sufficient. A large number of density functional approximations have been evaluated against the new reference data. The B2PLYP double hybrid gives the smallest deviations, but several functionals from different rungs of the usual ladder hierarchy give mean absolute deviations below 20 kJ/mol. This includes the B97-D semilocal functional, the PBE0* global hybrid with 15% exact-exchange admixture, as well as the local hybrids LH07s-SVWN and LH07t-SVWN. Several further functionals achieve mean absolute errors below 30 kJ/mol (M06L-D4, SSB-D, B97-1-D4, LC-ωPBE-D4, LH12ct-SsirPW92-D4, LH12ct-SsifPW92-D4, LH14t-calPBE-D4, LHJ-HFcal-D4, and several further double hybrids) and thereby also still overall outperform CCSD(T) or uncorrected CASPT2. While exact-exchange admixture is a crucial factor in favoring high-spin states, the present evaluations confirm that other aspects can be important as well. A number of the better-performing functionals underestimate the spin gaps for the π-acceptor ligands but overestimate them for L = NH₃, H₂O. In contrast to a previous suggestion, non-self-consistent density functional theory (DFT) computations on top of Hartree-Fock orbitals are not a promising path to produce accurate spin gaps in such complexes.

Environmental Control of the Magnetic Behavior of Transition Metal Complexes: Density Functional Theory Study of Zeolite Y Embedded Complexes [M(bpy)3]2+@Y (M = Fe2+, Co2+)

Using the supramolecular approach developed for the study of the guest-host interactions in the zeolite Y encapsulated [Fe(bpy)₃]²⁺ compound: [Fe(bpy)₃]²⁺@Y (bpy = 2,2'-bipyridine) [Vargas et al., J. Chem. Theory Comput. 2009, 5, 97-115], we apply density functional theory (DFT) to the study of the influence of zeolite Y encapsulation on the structural and energetic properties of [Co(bpy)₃]²⁺ in the low-spin (LS) and high-spin (HS) states, while revisiting [Fe(bpy)₃]²⁺@Y. Although the accurate prediction of the HS-LS energy difference ΔE_HL^el remains challenging for current DFT methods, they give accurate estimates of its variation Δ(ΔE_HL^el) in a series of complexes of a given transition metal ion. Therefore, denoting [M(bpy)₃]²⁺@Y_SM as the supramolecular model of the inclusion compounds, the values of ΔE_HL^el for the bpy complexes in the gas phase and in the supercage of zeolite Y were determined by combining the DFT estimates of Δ(ΔE_HL^el) in the series {[M(NCH)₆]²⁺, [M(bpy)₃]²⁺, and [M(bpy)₃]²⁺@Y_SM}, with accurate CCSD(T) estimates of ΔE_HL^el in the benchmark complexes [M(NCH)₆]²⁺ (M = Fe, Co) [Lawson Daku et al., J. Chem. Theory Comput., 2012, 8, 4216-4231]. Generalized gradient approximations as well as global and range-separated hybrids were employed. In order to better account for the key role of dispersion, they were also augmented with the semiempirical D2, D3BJ, and D3BJM dispersion corrections when available. The use of the D3BJ and D3BJM corrections led to similar results, and this is only with the use of the D2 scheme that (i) the free and encapsulated [Fe(bpy)₃]²⁺ are correctly predicted as LS species and that (ii) the encapsulation of both complexes translates into a destabilization of their HS state with respect to their LS state. The increase of the HS-LS energy difference is smaller for [Co(bpy)₃]²⁺ than [Fe(bpy)₃]²⁺ because the HS-LS molecular volume difference ΔV_HL in [Co(bpy)₃]²⁺ is ∼50% smaller than in [Fe(bpy)₃]²⁺. Periodic DFT calculations performed on crystalline [M(bpy)₃]²⁺@Y show that the employed [M(bpy)₃]²⁺@Y_SM supramolecular model allows the influence of encapsulation on the geometry and the spin-state energetics of [M(bpy)₃]²⁺ (M = Fe, Co) to be quantitatively captured.

Preliminary observations of the interplay of radiation damage with spin crossover

Intense synchrotron radiation makes time-resolved structural experiments with increasingly finer time sampling possible. On the other hand, radiation heating, radiation-induced volume change and structural disorder become more frequent. Temperature, volume change and disorder are known to be coupled with equilibrium in molecular spin complexes, balancing between two or more spin state configurations. Combining single-crystal diffraction and synchrotron radiation it is illustrated how the radiation damage and associated effects can affect the spin crossover process and may serve as yet another tool to further manipulate the spin crossover properties.

Trend in light-induced excited-state spin trapping in Fe(II)-based spin crossover systems

A computational study of the light-induced excited spin-state trapping (LIESST) in a number of Fe(II) spin crossover complexes, coordinated by monodentate, bidentate and multidentate ligands is carried out, with the goal to uncover the trend in the low temperature relaxation rate. A nine order of magnitude change in low temperature relaxation rate is observed among the complexes. The trend is rationalized in terms of the change in metal-ligand covalency, numerically estimated by the crystal orbital Hamiltonian population, thus influencing the back donation or delocalization of the electrons from the low-lying Fe(II)-centered molecular orbital to the empty low-lying ligand-centered π* antibonding molecular orbitals.

Accurate calculation of spin-state energy gaps in Fe(III) spin-crossover systems using density functional methods

Fe(III) complexes are receiving ever-increasing attention as spin crossover (SCO) systems because they are usually air stable, as opposed to Fe(II) complexes, which are prone to oxidation. Here, we present the first systematic study exclusively devoted to assess the accuracy of several exchange-correlation functionals when it comes to predicting the energy gap between the high-spin (S = 5/2) and the low-spin (S = 1/2) states of Fe(III) complexes. Using a dataset of 24 different Fe(III) hexacoordinated complexes, it is demonstrated that the B3LYP* functional is an excellent choice not only for predicting spin-state energy gaps for Fe(III) complexes undergoing spin-transitions but also for discriminating Fe(III) complexes that are either low- or high-spin in the whole range of temperatures. Our benchmark study has led to the identification of a very versatile Fe(III) compound whose SCO properties can be engineered upon changing a single axial ligand. Overall, this work demonstrates that B3LYP* is a reliable functional for screening new spin-crossover systems with tailored properties.

Fe(phen)2(NCS)2 on Al(100): influence of AlN layer on spin crossover barrier

We study how a nitride layer affects spin crossover (SCO) in a single Fe(phen)₂(NCS)₂ (Fephen) molecule adsorbed on the Al(100) surface using ab initio calculations. The Coulomb correlation of the open-shell 3d electrons has been considered using a Hubbard-U correction within different exchange-correlation approximations, including the van der Waals density functional. We determine the SCO energy barrier by computing the minimum energy path between the high-spin (HS) and low-spin (LS) states via direct constraint relaxations. It is shown that the HS-LS energy difference is slightly increased once deposited on Al(100), and thus LS states tend to be stabilized, as usually observed on metallic substrates. The oxidation of metallic Al to aluminum ions in the AlN layer promotes molecular adsorption, while it decreases HS-LS splitting, making Fephen switchable between its two spin states. Due to enhanced molecule-substrate bonding, the SCO barrier height is considerably increased, which may promote cooperativity. This effect is consistent with the AlN facilitated charge transfer at the interface that results from a reduction in surface work function. Our findings reveal the crucial role that surface electronic structure plays in maintaining spin bistability of the molecular adsorbate.

On the Spin-State Dependence of Redox Potentials of Spin Crossover Complexes

Resistance switching properties of nanoscale junctions of spin crossover molecules have received recently much interest. In many cases, this property has been traced back to the variation of molecular orbital energies upon spin transition. However, one can also expect a substantial reorganization of the molecular structure due to charge localization, which calls for a better understanding of the relationship between the redox potential and the spin state of the molecule. To investigate this issue, we carried out a detailed density functional theory and variable temperature cyclic voltammetry investigation of the benchmark compound [Fe(HB(1,2,4-triazol-1-yl)₃)₂] in solution. We show that, for a correct thermodynamical picture, it is necessary to take into account the charge transfer-induced electronic and structural reorganization as well as spin equilibria in the oxidized and reduced species.

Thermal spin crossover in Fe(ii) and Fe(iii). Accurate spin state energetics at the solid state

Parametrization of PBE+U under the D3 and D3-BJ dispersion corrections to study Fe^II and Fe^III-based Spin Crossover complexes.

Single-ion anisotropy and exchange coupling in cobalt(ii)-radical complexes: insights from magnetic and ab initio studies

The concurrent effects of single-ion anisotropy and exchange interactions on the electronic structure and magnetization dynamics have been analyzed for a cobalt(ii)-semiquinonate complex. Analogs containing diamagnetic catecholate and tropolonate ligands were employed for comparison of the magnetic behavior and zinc congeners assisted with the spectroscopic characterization and assessment of intermolecular interactions in the cobalt(ii) compounds. Low temperature X-band (ν ≈ 9.4 GHz) and W-Band (ν ≈ 94 GHz) electron paramagnetic resonance spectroscopy and static and dynamic magnetic measurements have been used to elucidate the electronic structure of the high spin cobalt(ii) ion in [Co(Me3tpa)(Br4cat)] (1; Me3tpa = tris[(6-methyl-2-pyridyl)methyl]amine, Br4cat2- = tetrabromocatecholate) and [Co(Me3tpa)(trop)](PF6) (2(PF6); trop- = tropolonate), which show slow relaxation of the magnetization in applied field. The cobalt(ii)-semiquinonate exchange interaction in [Co(Me3tpa)(dbsq)](PF6)·tol (3(PF6)·tol; dbsq- = 3,5-di-tert-butylsemiquinonate, tol = toluene) has been determined using an anisotropic exchange Hamiltonian in conjunction with multistate restricted active space self-consistent field ab initio modeling and wavefunction analysis, with comparison to magnetic and inelastic neutron scattering data. Our results demonstrate dominant ferromagnetic exchange for 3+ that is of similar magnitude to the anisotropy parameters of the cobalt(ii) ion and contains a significant contribution from spin-orbit coupling. The nature of the exchange coupling between octahedral high spin cobalt(ii) and semiquinonate ligands is a longstanding question; answering this question for the specific case of 3+ has confirmed the considerable sensitivity of the exchange to the molecular structure. The methodology employed will be generally applicable for elucidating exchange coupling between orbitally-degenerate metal ions and radical ligands and relevant to the development of bistable molecules and their integration into devices.

Calculating spin crossover temperatures by a first-principles LDA+U scheme with parameter U evaluated from GW

The prediction of spin crossover (SCO) temperatures (T_1/2) depends sensitively on the description of local Coulomb correlation. Due to its balance between accuracy and computational cost, local density approximation combined with Hubbard U model (LDA+U) is an appealing tool for this purpose. Despite its accurate performance on energetic properties, such as spin adiabatic energy difference, it is well-known that the LDA+U approach would lose its predictive power if U is tuned to achieve close agreement with experiment for a certain property. On the other hand, a static U value cannot account for changes in the electronic structure. Here, we propose a framework to derive dynamical U (U_dyn) values for iron(ii) complexes from the many-body GW calculations. By performing model calculations on a series of compounds with varying ligand fields, we show that the U values determined in this way are local environment dependent, and the resulting LDA+U_dyn method could reproduce their experimental ground spin states. We present applications to selected SCO complexes illustrating that U_dyn considerably overcomes some of the drawbacks of employing a constant U in the calculation of thermochemical quantities. Using the described calculation procedure, the T_1/2 values are predicted with a small mean absolute error of 176 K with respect to experiment.

DFT Study of the CNS Ligand Effect on the Geometry, Spin-State, and Absorption Spectrum in Ruthenium, Iron, and Cobalt Quaterpyridine Complexes

Geometry parameters, total energy of the system in different spin states, harmonic vibrational frequencies, and absorption spectra were computed for a range of mononuclear quaterpyridine Ru(II), Fe(III/II), and Co(III/II) complexes with two axial ambidentate CNS ligands by using density functional theory (DFT) and time-dependent DFT calculations. Both structural and electronic properties were found to be correlating with the type of the binding atom in the CNS ligand (isomerization differs by 4-13 kcal·mol-1). The N-bonding of CNS ligands is energetically favored. It was also found that the low spin (LS) state is the ground state for both Ru(II) and Co(III) complexes regardless of the CNS arrangement. The other complexes are the high-spin (HS) ground-state ones with the only exception of the S-bonded CNS isomer of the Fe(III) complex. The dependencies of energy differences between the HS and LS states versus C demonstrated stabilization of the HS state with an increasing amount of the exact exchange admixture (C) for iron and cobalt complexes. An opposite behavior was observed for ruthenium complexes. The best match in harmonic vibrational frequencies between the experimental and calculated values has been reached at C = 0.15 for all the complexes. The absorption profile of the Fe(II) complex with the alternatively bonded CNS ligands strongly depends on the angle between them. The light-harvesting efficiency of the Fe(II) complexes is very similar (∼0.4) and sufficiently close to that of the Ru(II) complexes. The iron-based coordination compounds are considered as a prospective dye for dye-sensitized solar cells. The results of calculations were completed with experimental reference data, thus providing a systematic compendium for practical use.

Spin trapping and flipping in FeCO through relativistic electron dynamics

Transition metal compounds are very versatile, and their characteristics can differ profoundly depending on their electronic structure. Compounds in which a spin transition from a low-spin to a high-spin state can be achieved through means of an optical excitation are particularly intriguing, as a controlled spin-flip opens promising avenues in areas such as sensing, information technology, molecular switches and energy technology. The fundamental mechanisms in spin crossover and spin transitions remain unanswered, due to the complexity of electronic structure and interplay of relativistic effects. Presented here is a new approach that allows the first direct study of spin flip dynamics through a mapping of spin-mixed to spin-pure states. The method is applied to FeCO and addresses the spin-flip dynamics during a spin transition. Wave packets that combine different spin states are generated through optical excitation and relevant mechanisms in optically triggered spin transitions are discussed.

Benchmarking quantum chemistry methods for spin-state energetics of iron complexes against quantitative experimental data

The accuracy of relative spin-state energetics predicted by selected quantum chemistry methods: coupled cluster theory at the CCSD(T) level, multiconfigurational perturbation theory (CASPT2, NEVPT2), multireference configuration interaction at the MRCISD+Q level, and a number of DFT methods, is quantitatively evaluated by comparison with the experimental data of four octahedral iron complexes. The available experimental data, either spin-forbidden transition energies or spin crossover enthalpies, are corrected for relevant environmental effects in order to derive the quantitative benchmark set of iron spin-state energetics. Comparison of theory predictions with the resulting reference data: (1) validates the high accuracy of the CCSD(T) method, particularly when based on Kohn-Sham orbitals, giving the maximum error below 2 kcal mol-1 and the mean absolute error (MAE) below 1 kcal mol-1; (2) corroborates the tendency of CASPT2 to systematically overstabilize higher-spin states by up to 5.5 kcal mol-1; (3) confirms that the latter problem is partly remedied by the recently proposed CASPT2/CC approach [Phung et al., J. Chem. Theory Comput., 2018, 14, 2446-2455]; (4) demonstrates that NEVPT2 performs worse than CASPT2, by giving errors up to 7 kcal mol-1; (5) shows that the accuracy of MRCISD+Q spin-state energetics strongly depends on the size-consistency correction: the Davidson-Silver and Pople corrections perform best (MAE < 3 kcal mol-1), whereas the standard Davidson correction is not recommended (MAE of 7 kcal mol-1). Only a few DFT methods (including the best performing ones identified in this study: B2PLYP-D3 and OPBE) are able to provide a balanced description of the spin-state energetics for all four studied iron complexes simultaneously, corroborating the non-universality problem of approximate density functionals.

High-temperature Spin Crossover of a Solvent-Free Iron(II) Complex with the Linear Hexadentate Ligand [Fe(L2-3-2Ph)](AsF6)2 (L2-3-2Ph = bis[N-(1-Phenyl-1H-1,2,3-triazol-4-yl)methylidene-2-aminoethyl]-1,3- propanediamine)

A novel mononuclear iron(II) complex with a linear hexadentate N6 ligand, containing two 1,2,3-triazole moieties, [Fe(L2-3-2Ph)](AsF6)2 (1), was synthesized (L2-3-2Ph = bis[N-(1-Phenyl-1H-1,2,3-triazol-4-yl)methylidene-2-aminoethyl]-1,3-propanediamine). Variable-temperature magnetic susceptibility measurements revealed a gradual one-step spin crossover (SCO) between the high-spin (HS, S = 2) and low-spin (LS, S = 0) states above room temperature (T1/2 = 468 K). The spin transition was further confirmed by differential scanning calorimetry (DSC). A single-crystal X-ray diffraction study showed that the complex was in the LS state (S = 0) at room temperature (296 K). In the crystal lattice, a three-dimensional (3D) supramolecular network was formed by intermolecular CH⋯ and – interactions of neighboring complex cations [Fe(L2-3-2Ph)]2+. AsF6− ions were located interstitially in the 3D network of complex cations, with no solvent-accessible voids. The crystal structure at 448 K (mixture of HS and LS species) was also successfully determined thanks to the thermal stability of the solvent-free crystal.

Transport property of ligand-driven light-induced spin-change Fe-based spin crossover complexes

The Fe-based spin-crossover (SCO) complexes, especially the ligand-driven light-induced spin-change (LD-LISC) systems with high spin-transition temperature, are considered as the most promising building blocks for designing molecular spintronic devices due to their bistability between the high-spin (HS) and low-spin (LS) states. Here, we explore the transport properties of Fe(stpy)₄(NCS)₂ LD-LISC SCO complexes with the trans and cis configurations sandwiched between Au electrodes by performing extensive density functional theory calculations combined with the non-equilibrium Green's function method. As for the trans configuration, the current through the molecular junction with the HS state is significantly larger than that of the LS state, which indicates that this Fe-based LD-LISC SCO complex with the trans configuration could act as a molecular switch when the spin transition is triggered by external stimuli. Remarkably, we observe the nearly perfect spin-filtering effect and obvious negative differential resistance feature in the Fe(stpy)₄(NCX)₂ junctions with the trans and cis configurations, which is attributed by the dramatically different electronic structures of two spin channels and the bias-dependent transmission spectra, respectively. These obtained theoretical findings suggest that the examined Fe-based LD-LISC SCO complexes hold great potential in molecular spintronics.

The transport properties of LD-LISC Fe-based SCO complexes with the trans and cis configuration exhibit robust spin-filtering and NDR features, which highlight them for promising applications in molecular devices.

Observation of the First Spin Crossover in an Iron(II) Complex with an S6 Coordination Environment: Tris[bis(N,N-diethylamino)carbeniumdithiocarboxylato]iron(II) Hexafluorophosphate

For the first time, the spin-crossover (SCO) phenomenon has been observed in an Fe^II -S₆ system in a tris(chelate)-type iron(II) complex with a zwitterionic sulfur donor bidentate, bis(N,N-diethylamino)carbeniumdithiocarboxylate (EtL), [Fe^II (EtL)₃ ](PF₆ )₂ (1), as synthesized by the reaction of a precursor complex [Fe^II (CH₃ CN)₆ ](PF₆ )₂ with EtL. In the solid state, the high-spin (HS) d⁶ state at ambient temperature and the low-spin (LS) d⁶ state at temperatures lower than approximately 240 K were evidenced by magnetic measurements with SQUID and Mössbauer spectra in the temperature range 4-290 K. X-ray analyses of the crystals at various temperatures disclosed that the distorted trigonal prismatic coordination environments essentially do not change; however, contraction of Fe-S distances by approximately 10 % (0.22 Å), ordering of alkyl groups in EtL and PF₆ ^- counteranions, and formation of significant intermolecular S⋅⋅⋅S interactions between adjacent molecules (average distances of 3.59 Å) take place during the transition from the HS to the LS state. A large decrease in the volume of the formula unit (78.1 ų ) might be responsible for the large activation barrier, thereby resulting in a slow phase transition upon cooling.

Tuning the Redox Potentials and Ligand Field Strength of Fe(II) Polypyridines: The Dual π-Donor and π-Acceptor Character of Bipyridine

The quintet-singlet energy difference (Δ E_Q/S) in Fe(II) polypyridine complexes is often interpreted in terms of metal-ligand π interactions. DFT calculations on a series of substituted [Fe(bpy)₃]²⁺ (bpy = 2,2'-bipyridine) complexes show the disparate magnitudes of substituent effects on tuning Δ E_Q/S and reduction potentials ( E°). In this series, E° spans a much larger range than Δ E_Q/S (2.07 vs 0.29 eV). While small changes in Δ E_Q/S are controlled by metal-ligand π interactions, large changes in E° arise from modification of the electrostatic environment around the Fe center. Molecular orbital analysis reveals that, contrary to the typical description of bpy as a π-acceptor, bpy is better described as acting as both a π-donor and π-acceptor in [Fe(bpy)₃]²⁺ complexes, even when it is substituted with highly electron withdrawing substituents. Overall, substituent modification is a useful strategy for fine-tuning the ligand field strength but not for significant reordering of the spin-state manifold, despite the large effect on metal-ligand electrostatic interactions.

Driving spin transition at interface: Role of adsorption configurations

A clear insight into the electrical manipulation of molecular spins at interface is crucial to the design of molecule-based spintronic devices. Here we report on the electrically driven spin transition in manganocene physisorbed on a metallic surface in two different adsorption configurations predicted by ab initio techniques, including a Hubbard-U correction at the manganese site and accounting for the long-range van der Waals interactions. We show that the application of an electric field at the interface induces a high-spin to low-spin transition in the flat-lying manganocene, while it could hardly alter the high-spin ground state of the standing-up molecule. This phenomenon cannot be explained by either the molecule-metal charge transfer or the local electron correlation effects. We demonstrate a linear dependence of the intra-molecular spin-state splitting on the energy difference between crystal-field splitting and on-site Coulomb repulsion. After considering the molecule-surface binding energy shifts upon spin transition, we reproduce the obtained spin-state energetics. We find that the configuration-dependent responses of the spin-transition originate from the binding energy shifts instead of the variation of the local ligand field. Through these analyses, we obtain an intuitive understanding of the effects of molecule-surface contact on spin-crossover under electrical bias.

Iron(II) and Iron(III) Spin Crossover: Toward an Optimal Density Functional

Spin crossover (SCO) plays a major role in biochemistry, catalysis, materials, and emerging technologies such as molecular electronics and sensors, and thus accurate prediction and design of SCO systems is of high priority. However, the main tool for this purpose, density functional theory (DFT), is very sensitive to applied methodology. The most abundant SCO systems are Fe(II) and Fe(III) systems. Even with average good agreement, a functional may be significantly more accurate for Fe(II) or Fe(III) systems, preventing balanced study of SCO candidates of both types. The present work investigates DFT's performance for well-known Fe(II) and Fe(III) SCO complexes, using various design types and customized versions of GGA, hybrid, meta-GGA, meta-hybrid, double-hybrid, and long-range-corrected hybrid functionals. We explore the limits of DFT performance and identify proficient Fe(II)-Fe(III)-balanced functionals. We identify and quantify remarkable differences in the DFT description of Fe(II) and Fe(III) systems. Most functionals become more accurate once Hartree-Fock exchange is adjusted to 10-17%, regardless of the type of functionals involved. However, this typically introduces a clear Fe(II)-Fe(III) bias. The most accurate functionals measured by mean absolute errors <10 kJ/mol are CAMB3LYP-17, B3LYP*, and B97-15 with 15-17% Hartree-Fock exchange, closely followed by CAMB3LYP and CAMB3LYP-15, OPBE, rPBE-10, and B3P86-15. While GGA functionals display a small Fe(II)-Fe(III) bias, they are generally inaccurate, except the O exchange functional. Hybrid functionals (including B2PLYP double hybrids and meta hybrids) tend to favor HS too much in Fe(II) vs Fe(III), which is important in many studies where the oxidation state of iron can vary, e.g. rational SCO design and studies of catalytic processes involving iron. The only functional with a combined bias <5 kJ/mol and a decent MAE (15 kJ/mol) is our customized PBE0-12 functional. Alternatively one has to sacrifice Fe(II)-Fe(III) balance to use the best functionals for each group separately. We also investigated the precision (measured as the standard deviation of errors) and show that the target accuracy for iron SCO is 10 kJ/mol for accuracy and 5 kJ/mol for precision, and DFT is probably not going to break this limit in the near future. Importantly, all four types of functional behavior (accurate/precise, accurate/imprecise, inaccurate/precise, inaccurate/imprecise) are observed. More generally, our work illustrates the importance not only of overall accuracy but also of balanced accuracy for systems likely to occur in context.

Nuclear inelastic scattering and density functional theory studies of a one-dimensional spin crossover [Fe(1,2,4-triazole)2(1,2,4-triazolato)](BF4) molecular chain

Nuclear inelastic scattering (NIS) experiments have been performed in order to study the vibrational dynamics of the low- and high-spin states of the polynuclear 1D spin crossover compound [Fe(1,2,4-triazole)₂(1,2,4-triazolato)](BF₄) (1). Density functional theory (DFT) calculations using the functional B3LYP* and the basis set CEP-31G for heptameric and nonameric models of the compound yielded the normal vibrations and electronic energies for high-spin and low-spin isomers of three models differing in the distribution of anionic trz^- ligands and BF₄^- anions. On the basis of the obtained energies a structural model with a centrosymmetric Fe(trzH)₄(trz^-)₂ coordination core of the mononuclear unit of the chain is proposed. The obtained distribution of the BF₄^- counteranions in the proposed structure is similar to that obtained on the basis of X-ray powder diffraction studies by Grossjean et al. (Eur. J. Inorg. Chem., 2013, 796). The NIS data of the system diluted to 10% Fe(ii) content in a 90% Zn(ii) matrix (compound (2)) show a characteristic change of the spectral pattern of the low-spin centres, compared to the low-spin phase of the parent Fe(ii) complex (1). DFT calculations reveal that this is caused by a change of the structure of the neighbours of the low-spin centres. The spectral pattern of the high-spin centres in (2) is within a good approximation identical to that of the high-spin Fe(ii) isomer of (1). The inspection of the molecular orbitals of the monomeric model systems of [Fe(trzH)₄(trz^-)₂] and [Fe(trzH)₆], together with calculations of spin transition energies, point towards the importance of an electrostatic effect caused by the negatively charged ligands. This results in the stabilisation of the low-spin state of the complex containing the anionic ligand and shortening of the Fe-N(trz^-) compared to the Fe-N(trzH) bond in high-spin, but not in low-spin [Fe(trzH)₄(trz^-)₂].

A Simple Approach for Predicting the Spin State of Homoleptic Fe(II) Tris-diimine Complexes

We propose a simple method for predicting the spin state of homoleptic complexes of the Fe(II) d⁶ ion with chelating diimine ligands. The approach is based on the analysis of a single metric parameter within a free (noncoordinated) ligand: the interatomic separation between the N-donor metal-binding sites. An extensive analysis of existing complexes allows the determination of critical N···N distances that dictate the regions of stability for the high-spin and low-spin complexes, as well as the intermediate range in which the magnetic bistability (spin crossover) can be observed. The prediction has been tested on several complexes that demonstrate the validity of our method.

Cooperativity of Spin Crossover Complexes: Combining Periodic Density Functional Calculations and Monte Carlo Simulation

The total enthalpies of the 16 different spin configurations that can be realized in the unit cell of the archetype spin crossover complex [Fe(phen)2(NCS)2] (phen = 1,2-phenanthroline) were calculated, applying periodic density functional theory combined with the Hubbard model and the Grimme-D2 dispersion correction (DFT+U+D2). The obtained enthalpy differences between the individual spin configurations were used to determine spin couplings of an Ising-like model, and subsequent Monte Carlo simulations for this model allowed the estimation of the phenomenological interaction parameter Γ of the Slichter–Drickamer model, which is commonly used to describe the cooperativity of the spin transition. The calculation procedure described here—which led to an estimate of about 3 kJ·mol−1 for Γ, in good agreement with experiment—may be used to predict from first principles how modifications of spin crossover complexes can change the character of the spin transition from gradual to abrupt and vice versa.

A Redox-Induced Spin-State Cascade in a Mixed-Valent Fe3 (μ3 -O) Triangle

One-electron reduction of a pyrazolate-bridged triangular Fe₃ (μ₃ -O) core induces a cascade wherein all three metal centers switch from high-spin Fe³⁺ to low-spin Fe^2.66+ . This hypothesis is supported by spectroscopic data (¹ H-NMR, UV-vis-NIR, infra-red, ⁵⁷ Fe-Mössbauer, EPR), X-ray crystallographic characterization of the cluster in both oxidation states and also density functional theory. The reduction induces substantial contraction in all bond lengths around the metal centers, along with diagnostic shifts in the spectroscopic parameters. This is, to the best of our knowledge, the first example of a one-electron redox event causing concerted change in multiple iron centers.

Diffusion Monte Carlo Perspective on the Spin-State Energetics of [Fe(NCH)6](2.)

The energy difference between the high spin and the low spin state of the model compound [Fe(NCH)6](2+) is investigated by means of Diffusion Monte Carlo (DMC), where special attention is dedicated to analyzing the effect of the fix node approximation on the accuracy of the results. For this purpose, we compare several Slater-Jastrow and multireference Slater-Jastrow trial wave functions. We found that a Slater-Jastrow trial wave function constructed with the generalized Kohn-Sham orbitals from hybrid DFT represents the optimal choice. This is understood by observing that hybrid functionals account for the subtle balance between exchange and correlation effects and the respective orbitals accurately describe the ligand-metal hybridization as well as the charge reorganization accompanying the spin transition. Finally the DMC results are compared with those obtained by Hartree-Fock, DFT, CASSCF, and CASPT2. While there is no clear reference value for the high spin-low spin energy difference, DMC and high level CCSD(T) calculations agree within around 0.3 eV.

Theoretical Study of Spin Crossover in 30 Iron Complexes

Iron complexes are important spin crossover (SCO) systems with vital roles in oxidative metabolism and promising technological potential. The SCO tendency depends on the free energy balance of high- and low-spin states, which again depends on physical effects such as dispersion, relativistic effects, and vibrational entropy. This work studied 30 different iron SCO systems with experimentally known thermochemical data, using 12 different density functionals. Remarkably general entropy-enthalpy compensation across SCO systems was identified (R = 0.82, p = 0.002) that should be considered in rational SCO design. Iron(II) complexes displayed higher ΔH and ΔS values than iron(III) complexes and also less steep compensation effects. First-coordination sphere ΔS values computed from numerical frequencies reproduce most of the experimental entropy and should thus be included when modeling spin-state changes in inorganic chemistry (R = 0.52, p = 3.4 × 10(-3); standard error in TΔS ≈ 4.4 kJ/mol at 298 K vs 16 kJ/mol of total TΔS on average). Zero-point energies favored high-spin states by 9 kJ/mol on average. Interestingly, dispersion effects are surprisingly large for the SCO process (average: 9 kJ/mol, but up to 33 kJ/mol) and favor the more compact low-spin state. Relativistic effects favor low-spin by ∼9 kJ/mol on average, but up to 24 kJ/mol. B3LYP*, TPSSh, B2PLYP, and PW6B95 performed best for the typical calculation scheme that includes ZPE. However, if relativistic and dispersion effects are included, only B3LYP* remained accurate. On average, high-spin was favored by LYP by 11-15 kJ/mol relative to other correlation functionals, and by 4.2 kJ/mol per 1% HF exchange in hybrids. 13% HF exchange was optimal without dispersion, and 15% was optimal with all effects included for these systems.

Spin crossover properties of enantiomers, co-enantiomers, racemates, and co-racemates

Spin-crossover Puzzle: SCO co-enantiomers, racemates, and co-racemates were successfully assembled via cocrystallization of four prefabricated enantiomeric iron(ii) modules 4R, 4S, 5R and 5S.

Abrupt versus Gradual Spin-Crossover in Fe(II)(phen)2(NCS)2 and Fe(III)(dedtc)3 Compared by X-ray Absorption and Emission Spectroscopy and Quantum-Chemical Calculations

Molecular spin-crossover (SCO) compounds are attractive for information storage and photovoltaic technologies. We compared two prototypic SCO compounds with Fe(II)N6 (1, [Fe(phen)2(NCS)2], with phen = 1,10-phenanthroline) or Fe(III)S6 (2, [Fe(dedtc)3], with dedtc = N,N'-diethyldithiocarbamate) centers, which show abrupt (1) or gradual (2) thermally induced SCO, using K-edge X-ray absorption and Kβ emission spectroscopy (XAS/XES) in a 8-315 K temperature range, single-crystal X-ray diffraction (XRD), and density functional theory (DFT). Core-to-valence and valence-to-core electronic transitions in the XAS/XES spectra and bond lengths change from XRD provided benchmark data, verifying the adequacy of the TPSSh/TZVP DFT approach for the description of low-spin (LS) and high-spin (HS) species. Determination of the spin densities, charge distributions, bonding descriptors, and valence-level configurations, as well as similar experimental and calculated enthalpy changes (ΔH), suggested that the varying metal-ligand bonding properties and deviating electronic structures converge to similar enthalpic contributions to the free-energy change (ΔG) and thus presumably are not decisive for the differing SCO behavior of 1 and 2. Rather, SCO seems to be governed by vibrational contributions to the entropy changes (ΔS) in both complexes. Intra- and intermolecular interactions in crystals of 1 and 2 were identified by atoms-in-molecules analysis. Thermal excitation of individual dedtc ligand vibrations accompanies the gradual SCO in 2. In contrast, extensive inter- and intramolecular phen/NCS vibrational mode coupling may be an important factor in the cooperative SCO behavior of 1.